1. Field of the Invention
This invention generally relates to Orthogonal Frequency Division Multiple Access (OFDMA) and Single Carrier Frequency Division Multiple Access (SC-FDMA) communications, and more particularly, to system and method for estimating carrier frequency offset (CFO) and Doppler frequency shifts.
2. Description of the Related Art
FIG. 1 is a diagram depicting a Multiuser MIMO (MU-MIMO) wireless communication system (prior art). Multiple users can transmit data simultaneously at the same frequency to a multi-antenna base station, resulting in increased aggregate cell throughput. There is a need to decouple data streams from different users via MU-MIMO equalization, which requires MU-MIMO channel estimation.
FIG. 2 is a diagram depicting an exemplary MIMO receiver (prior art). Channel estimation is needed in multi-user and single-user MIMO receivers to separate different spatial streams and/or user signals via equalization. Of special interest is OFDMA and SC-FDMA multi-user MIMO channel estimation with a single spatial stream per user (e.g., LTE uplink). After cyclic pulse (CP) removal and a fast Fourier transform (FFT), the input to the channel estimator block is the received frequency domain signal of reference symbols from Mr number of receive antennas. The outputs are channel responses in the frequency domain from user u (1≦u≦U) to antenna m (0≦m≦Mr−1) are demodulated (demod) and decoded.
In SC-FDMA or OFDMA, carrier frequency offset (CFO) and Doppler frequency estimation and correction mitigate against the loss of orthogonality among subcarriers and users. Each user has a different CFO/Doppler frequency shift. Hence, CFO/Doppler estimation and correction should be done in the frequency domain on a per-user basis after user separation (which is performed by the equalizer).
Conventional methods of CFO compensation in OFDM include time-domain tracking loops, which are not feasible for OFDMA or SC-FDMA systems because each user has a different CFO. Other methods for OFDMA typically assume a certain frequency allocation for the user.
FIG. 3 is a diagram illustrating the source of CFO and Doppler frequency shift (prior art). CFO and Doppler frequency shift cause a linear phase rotation in time of the received signal. The combined CFO and Doppler frequency shift for user u is denoted by Δfu, whereΔfu=fRx−fTx,u 
The phase rotation causes constellations to rotate and results in higher block error rates.
The CFO/Doppler frequency shift can be modeled. The equivalent baseband signal model is as follows:
                              y          ⁡                      (            t            )                          =                ⁢                                            ⅇ                                                -                  j                                ⁢                                                                  ⁢                2                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                                  f                  Rx                                ⁢                t                                      ⁢                                          ∑                u                            ⁢                              ∫                                                                            h                      u                                        ⁡                                          (                                              t                        ,                        τ                                            )                                                        ⁢                                      ⅇ                                          j                      ⁢                                                                                          ⁢                      2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                                                                        f                                                      Tx                            ,                            u                                                                          ⁡                                                  (                                                      t                            -                            τ                                                    )                                                                                                      ⁢                                                            x                      u                                        ⁡                                          (                                              t                        -                        τ                                            )                                                        ⁢                                                                          ⁢                                      ⅆ                    τ                                                                                +                      w            ⁡                          (              t              )                                                              =                ⁢                                            ∑              u                        ⁢                                          ⅇ                                                      -                    j                                    ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                  π                  ⁢                                                                          ⁢                  Δ                  ⁢                                                                          ⁢                                      f                    u                                    ⁢                  t                                            ⁢                              ∫                                                                            h                      u                                        ⁡                                          (                                              t                        ,                        τ                                            )                                                        ⁢                                      ⅇ                                                                  -                        j                                            ⁢                                                                                          ⁢                      2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                                              f                                                  Tx                          ,                          u                                                                    ⁢                      τ                                                        ⁢                                                            x                      u                                        ⁡                                          (                                              t                        -                        τ                                            )                                                        ⁢                                                                          ⁢                                      ⅆ                    τ                                                                                +                      w            ⁡                          (              t              )                                                              =                ⁢                                            ∑              u                        ⁢                                          ⅇ                                                      -                    j                                    ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                  π                  ⁢                                                                          ⁢                  Δ                  ⁢                                                                          ⁢                                      f                    u                                    ⁢                  t                                            ⁢                              ∫                                                                                                    h                        ~                                            u                                        ⁡                                          (                                              t                        ,                        τ                                            )                                                        ⁢                                                            x                      u                                        ⁡                                          (                                              t                        -                        τ                                            )                                                        ⁢                                                                          ⁢                                      ⅆ                    τ                                                                                +                      w            ⁡                          (              t              )                                                                                    y            ⁡                          (              t              )                                ⁢                      :                    ⁢                       ⁢          received          ⁢                                          ⁢          signal          ⁢                                          ⁢          vector                ⁢                                                              x            u                    ⁡                      (            t            )                          ⁢                  :                ⁢                   ⁢        transmitted        ⁢                                  ⁢        signal        ⁢                                  ⁢        for        ⁢                                  ⁢        user        ⁢                                  ⁢        u                                                                    h              u                        ⁡                          (                              t                ,                τ                            )                                ⁢                      :                    ⁢                       ⁢          time                -                  varying          ⁢                                          ⁢          channel          ⁢                                          ⁢          impulse          ⁢                                          ⁢          response          ⁢                                          ⁢          for          ⁢                                          ⁢          user          ⁢                                          ⁢          u                                                  w          ⁡                      (            t            )                          ⁢                  :                ⁢                   ⁢        AWGN        ⁢                                  ⁢        vector            
Assuming the phase of the channel response is linear over time t, and the amplitude remains constant, the phase change from the channel can be absorbed into Δfu.
FIG. 4 is a diagram depicting a subframe consisting of two slots, as is used in Long Term Evolution (LTE) (prior art). LTE is the Third Generation Partnership Program (3GPP) term for the next generation cellular standard. The figure shows two resource blocks, with one resource block per slot. Each slot includes seven OFDMA or SC-FDMA symbols for normal CP, or 6 symbols for extended CP, at twelve subcarrier frequencies. In OFDMA and SC-FDMA, each user is allocated resource elements (REs) in time and frequency. SC-FDMA is similar to OFDMA except that user data are spread via a discrete Fourier transform (DFT) before OFDMA modulation. Each resource element consists of 1 subcarrier in the frequency domain and 1 OFDMA or SC-FDMA symbol in the time domain. User data modulates the amplitude and phase of each subcarrier for the duration of 1 OFDMA or SC-FDMA symbol. Multiple users can modulate the same RE (MU-MIMO). In the LTE uplink, each user transmits reference signals on all REs of specified symbols. Different user reference signals are multiplexed using different cyclic shifts. The base station uses the reference signals to estimate a channel for each user.
FIG. 5 is a diagram depicting an exemplary OFDMA frequency spectrum (prior art). OFDMA is a multi-user version of the popular Orthogonal frequency-division multiplexing (OFDM) digital modulation scheme. Multiple access is achieved in OFDMA by assigning subsets of subcarriers to individual users as shown. This allows simultaneous low data rate transmission from several users. OFDMA is recognized as being highly sensitive to frequency offsets and phase noise. OFDMA can also be described as a combination of frequency domain and time domain multiple access, where the resources are partitioned in the time-frequency space, and slots are assigned along the OFDM symbol index as well as OFDM sub-carrier index. OFDMA is considered as highly suitable for broadband wireless networks, due to advantages including scalability and MIMO-friendliness, and ability to take advantage of channel frequency selectivity.
SC-FDMA is a multi-user version of Single-carrier frequency-domain-equalization (SC-FDE) modulation scheme. SC-FDE can be viewed as a linearly precoded OFDM scheme, and SC-FDMA can be viewed as a linearly precoded OFDMA scheme, henceforth LP-OFDMA. FDE is the equalizer at receiver end. It is different from the modulation scheme. Or, it can be viewed as a single carrier multiple access scheme. Just like in OFDM, guard intervals with cyclic repetition are introduced between blocks of symbols in view to efficiently eliminate time spreading (caused by multi-path propagation) among the blocks. In OFDM, a Fast Fourier transform (FFT) is applied on the receiver side on each block of symbols, and inverse FFT (IFFT) on the transmitter side. In SC-FDE, both FFT and IFFT are applied on the receiver side, but not on the transmitter side. In SC-FDMA, both FFT and IFFT are applied on the transmitter side, and also on the receiver side.
In OFDM as well as SC-FDE and SC-FDMA, equalization is achieved on the receiver side after the FFT calculation, by multiplying each Fourier coefficient by a complex number. Thus, frequency-selective fading and phase distortion can be combated. The advantage is that FFT and frequency domain equalization requires less computation power than conventional time-domain equalization. In SC-FDMA, multiple access is made possible by inserting zero Fourier-coefficients on the transmitter side before the IFFT, and removing them on the receiver side after the FFT. Different users are assigned to different Fourier-coefficients (sub-carriers).
LTE uses OFDMA for the downlink—that is, from the base station to the terminal. In the time domain the radio frame is 10 ms long and consists of 10 sub frames of 1 ms each. In LTE with frequency-division duplexing (FDD), every sub frame consists of 2 slots where each slot is 0.5 ms. The subcarrier spacing in the frequency domain is 15 kHz and there are modes with 7.5 kHz subcarrier spacing. Twelve of these subcarriers together (per slot) are called a resource block, so one resource block is 180 kHz. 6 Resource blocks fit in a carrier of 1.4 MHz and 100 resource blocks fit in a carrier of 20 MHz. In the uplink, for the Physical Uplink Shared channel (PUSCH) only, LTE uses a pre-coded version of OFDMA called SC-FDMA to compensate for a drawback with normal OFDMA, which has a very high peak-to-average power ratio (PAPR). High PAPR requires expensive and inefficient power amplifiers with high requirements on linearity, which increases the cost of the terminal and drains the battery faster. SC-FDMA solves this problem by grouping together the resource blocks in a way that reduces the need for linearity, and so power consumption, in the power amplifier. A low PAPR also improves coverage and the cell-edge performance.
In MIMO systems, a transmitter sends multiple streams by multiple transmit antennas. The transmit streams go through a matrix channel which consists of all paths between the transmit antennas at the transmitter and receive antennas at the receiver. Then, the receiver gets the received signal vectors by the multiple receive antennas and decodes the received signal vectors into the original information. A narrowband flat fading MIMO system is modeled as:y=Hx+n 
where y and x are the receive and transmit vectors, respectively, and H and n are the channel matrix and the noise vector, respectively. Where x is a Mt×1 vector, y and n are Mr×1 vectors.
With respect to MU-MIMO channel estimation for OFDMA/SC-FDMA, user reference signals with different cyclic shifts are orthogonal across a number of tones in ideal scenarios (no timing offset and low delay spread). In this case, channel estimation for each user is decoupled. Several channel estimation techniques exist in prior art, such as least squares, minimum mean-square error (MMSE), discrete cosine transform (DCT), can be used under the orthogonality assumption. In practice, orthogonality is destroyed because of different user timing offsets and/or medium to high delay spreads.
FIG. 6 is a drawing depicting uplink reference signals in LTE (normal cyclic prefix) (prior art). The reference signals of the different users are orthogonal across a number of tones if the same base sequence is used and each user applies a unique cyclic shift. The demodulation reference signal (DM-RS) for each slot is assigned SC-FDMA symbol index 0. The DM-RS symbol is the phase reference since the equalizer is computed at the DM-RS symbol. Thus, degradation from phase rotation is worse for constellations in symbols further in time from the DM-RS symbol. The duration of each SC-FDMA symbol is Tsym. The duration of each slot is Tslot.
It would be advantageous if the effects of CFO and Doppler frequency shifting could be estimated in a receiver prior to demodulation and decoding.